Relaxation to nonequilibrium

Abstract

We describe the structure of relaxation for a steadily driven macroscopic body. The time-evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing the dynamical fluctuations. The approach hinges on two main elements: the principle of local detailed balance, which identifies the relevant thermodynamic forces, and the canonical decomposition of the frenesy into a Legendre pair. Notably, it is the time-symmetric component of the Lagrangian, the frenesy, that shapes the structure of the macroscopic evolution for given forcing. We add a simple argument for why the nonequilibrium entropy, which governs the static macroscopic fluctuations of the system, is monotone in time. The results can be interpreted as the steady nonequilibrium extension of GENERIC where relaxation to equilibrium is governed by a dissipative gradient flow superimposed on a Hamiltonian flow.